[Show abstract][Hide abstract] ABSTRACT: We discuss the use of Langevin molecular dynamics in the investigation of the
non-equilibrium properties of disordered vortex matter. Our special focus is
set on values of system parameters that are realistic for disordered high-$T_c$
superconductors such as YBCO. Using a discretized elastic line model, we study
different aspects of vortices far from thermal equilibrium. On the one hand we
investigate steady-state properties of driven magnetic flux lines in a
disordered environment, namely the current-voltage characteristics, the
gyration radius, and the pinning time statistics. On the other hand we study
the complex relaxation processes and glassy-like dynamics that emerge in
type-II superconductors due to the intricate competition between the long-range
vortex-vortex repulsion and flux pinning due to randomly placed point defects.
To this end we consider different types of sudden perturbations: temperature,
magnetic field, and external current quenches.
[Show abstract][Hide abstract] ABSTRACT: Vortex lines in type-II superconductors display complicated relaxation
processes due to the intricate competition between their mutual repulsive
interactions and pinning to attractive point or extended defects. We perform
extensive Monte Carlo simulations for an interacting elastic line model with
either point-like or columnar pinning centers. From measurements of the space-
and time-dependent height-height correlation function for lateral flux line
fluctuations, we extract a characteristic correlation length that we use to
investigate different non-equilibrium relaxation regimes. The specific time
dependence of this correlation length for different disorder configurations
displays characteristic features that provide a novel diagnostic tool to
distinguish between point-like pinning centers and extended columnar defects.
Journal of Statistical Mechanics Theory and Experiment 07/2015; 2015(9). DOI:10.1088/1742-5468/2015/09/P09010 · 2.40 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We study the effects of rapid temperature and magnetic field changes on the
non-equilibrium relaxation dynamics of magnetic vortex lines in disordered
type-II superconductors by employing an elastic line model and performing
Langevin molecular dynamics simulations. In a previously equilibrated system,
either the temperature is suddenly changed, or the magnetic field is
instantaneously altered which is reflected in adding or removing flux lines to
or from the system. The subsequent aging properties are investigated in samples
with either randomly distributed point-like or extended columnar defects, which
allows to distinguish the complex relaxation features that result from either
type of pinning centers. One-time observables such as the radius of gyration
and the fraction of pinned line elements are employed to characterize
steady-state properties, and two-time correlation functions such as the vortex
line height autocorrelations and their mean-square displacement are analyzed to
study the non-linear stochastic relaxation dynamics in the aging regime.
[Show abstract][Hide abstract] ABSTRACT: We consider cyclic Lotka-Volterra models with three and four strategies where
at every interaction agents play a strategy using a time-dependent probability
distribution. Agents learn from a loss by reducing the probability to play a
losing strategy at the next interaction. For that, an agent is described as an
urn containing $\beta$ balls of three respectively four types where after a
loss one of the balls corresponding to the losing strategy is replaced by a
ball representing the winning strategy. Using both mean-field rate equations
and numerical simulations, we investigate a range of quantities that allow us
to characterize the properties of these cyclic models with time-dependent
probability distributions. For the three-strategy case in a spatial setting we
observe a transition from neutrally stable to stable when changing the level of
discretization of the probability distribution. For large values of $\beta$,
yielding a good approximation to a continuous distribution, spatially
synchronized temporal oscillations dominate the system. For the four-strategy
game the system is always neutrally stable, but different regimes emerge,
depending on the size of the system and the level of discretization.
Physical Review E 02/2015; 91(5). DOI:10.1103/PhysRevE.91.052135 · 2.29 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We discuss relaxation and aging processes in the one- and two-dimensional
$ABC$ models. In these driven diffusive systems of three particle types, biased
exchanges in one direction yield a coarsening process characterized by a
logarithmic growth of ordered domains that take the form of stripes. From the
time-dependent length, derived from the equal-time spatial correlator, and from
the mean displacement of individual particles different regimes in the
formation and growth of these domains can be identified. Analysis of two-times
correlation and response functions reveals dynamical scaling in the asymptotic
logarithmic growth regime as well as complicated finite-time and finite-size
effects in the early and intermediate time regimes.
Physical Review E 02/2015; 91(5). DOI:10.1103/PhysRevE.91.052116 · 2.29 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The statistical mechanics of a one-dimensional Ising model in thermal
equilibrium is well-established, textbook material. Yet, when driven far from
equilibrium by coupling two sectors to two baths at different temperatures, it
exhibits remarkable phenomena, including an unexpected 'freezing by heating.'
These phenomena are explored through systematic numerical simulations. Our
study reveals complicated relaxation processes as well as a crossover between
two very different steady-state regimes.
Physical Review E 11/2014; 90(6). DOI:10.1103/PhysRevE.90.062113 · 2.29 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Synthetic antiferromagnets with strong perpendicular anisotropy can be
modeled by layered Ising antiferromagnets. Accounting for the fact that in the
experimental systems the ferromagnetic layers, coupled antiferromagnetically
via spacers, are multilayers, we propose a description through Ising films
where ferromagnetic stacks composed of multiple layers are coupled
antiferromagnetically. We study the equilibrium and non-equilibrium properties
of these systems where we vary the number of layers in each stack. Using
numerical simulations, we construct equilibrium temperature$-$magnetic field
phase diagrams for a variety of cases. We find the same dominant features
(three stable phases, where one phase boundary ends in a critical end point,
whereas the other phase boundary shows a tricritical point at which the
transition changes from first to second order) for all studied cases. Using
time-dependent quantities, we also study the ordering processes that take place
after a temperature quench. The nature of long-lived metastable states are
discussed for thin films, whereas for thick films we compute the surface
autocorrelation exponent.
Physical Review B 07/2014; 90(1). DOI:10.1103/PhysRevB.90.014438 · 3.74 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We study the pinning dynamics of magnetic flux (vortex) lines in a disordered
type-II superconductor. Using numerical simulations of a directed elastic line
model, we extract the pinning time distributions of vortex line segments. We
compare different model implementations for the disorder in the surrounding
medium: discrete, localized pinning potential wells that are either attractive
and repulsive or purely attractive, and whose strengths are drawn from a
Gaussian distribution; as well as continuous Gaussian random potential
landscapes. We find that both schemes yield power law distributions in the
pinned phase as predicted by extreme-event statistics, yet they differ
significantly in their effective scaling exponents and their short-time
behavior.
Physical Review E 05/2014; 90(6). DOI:10.1103/PhysRevE.90.062108 · 2.29 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We employ Monte Carlo simulations to investigate the non-equilibrium
relaxation properties of the two- and three-dimensional Coulomb glass with
different long-range repulsive interactions. Specifically, we explore the aging
scaling laws in the two-time density autocorrelation function. We find that in
the time window and parameter range accessible to us, the scaling exponents are
not universal, depending on the filling fraction and temperature: As either the
temperature decreases or the filling fraction deviates more from half-filling,
the exponents reflect markedly slower relaxation kinetics. In comparison with a
repulsive Coulomb potential, appropriate for impurity states in strongly
disordered semiconductors, we observe that for logarithmic interactions, the
soft pseudo-gap in the density of states is considerably broader, and the
dependence of the scaling exponents on external parameters is much weaker. The
latter situation is relevant for flux creep in the disorder-dominated Bose
glass phase of type-II superconductors subject to columnar pinning centers.
Physical Review E 03/2014; 90(3-1). DOI:10.1103/PhysRevE.90.032111 · 2.29 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: In order to model real ecological systems one has to consider many species
that interact in complex ways. However, most of the recent theoretical studies
have been restricted to few species systems with rather trivial interactions.
The few studies dealing with larger number of species and/or more complex
interaction schemes are mostly restricted to numerical explorations. In this
paper we determine, starting from the deterministic mean-field rate equations,
for large classes of systems the space of coexistence fixed points at which
biodiversity is maximal. For systems with a single coexistence fixed point we
derive complex Ginzburg-Landau equations that allow to describe space-time
pattern realized in two space dimensions. For selected cases we compare the
theoretical predictions with the pattern observed in numerical simulations.
Journal of Physics A Mathematical and Theoretical 03/2014; 47(16). DOI:10.1088/1751-8113/47/16/165001 · 1.58 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We study the surface phase diagram of the three-dimensional kinetic Ising
model below the equilibrium critical point subjected to a periodically
oscillating magnetic field. Changing the surface interaction strength as well
as the period of the external field, we obtain a non-equilibrium surface phase
diagram that in parts strongly resembles the corresponding equilibrium phase
diagram, with an ordinary transition, an extraordinary transition and a surface
transition. These three lines meet at a special transition point. For weak
surface couplings, however, the surface does not order. These results are found
to remain qualitatively unchanged when using different single-spin flip
dynamics.
Physical Review E 02/2014; 89(2). DOI:10.1103/PhysRevE.89.022121 · 2.29 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We consider the non-conserved dynamics of the Ising model on the
two-dimensional square lattice, where each spin is influenced preferentially by
its East and North neighbours. The single-spin flip rates are such that the
stationary state is Gibbsian with respect to the usual ferromagnetic Ising
Hamiltonian. We show the existence, in the paramagnetic phase, of a dynamical
transition between two regimes of violation of the fluctuation-dissipation
theorem in the nonequilibrium stationary state: a regime of weak violation
where the stationary fluctuation-dissipation ratio is finite, when the
asymmetry parameter is less than a threshold value, and a regime of strong
violation where this ratio vanishes asymptotically above the threshold. The
present study suggests that this novel kind of dynamical transition in
nonequilibrium stationary states, already found for the directed Ising chain
and the spherical model with asymmetric dynamics, might be quite general. In
contrast with the later models, the equal-time correlation function for the
two-dimensional directed Ising model depends on the asymmetry.
Journal of Statistical Mechanics Theory and Experiment 01/2014; 2014(5). DOI:10.1088/1742-5468/2014/05/P05005 · 2.40 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Systems with a bulk first-order transition can display diverging correlation
lengths close to a surface. This surface induced disordering yields a special
type of surface criticality. Using extensive numerical simulations we study
surface quantities in the two-dimensional Potts model with a large number of
states $q$ which undergoes a discontinuous bulk transition. The surface
critical exponents are thereby found to depend on the value of $q$, which is in
contrast to prior claims that these exponents should be universal and
independent of $q$. It follows that surface induced disordering at first-order
transitions is characterized by exponents that depend on the details of the
model.
Physical Review B 11/2013; 88(21). DOI:10.1103/PhysRevB.88.214426 · 3.74 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: When four species compete stochastically in a cyclic way, the formation of
two teams of mutually neutral partners is observed. In this paper we study
through numerical simulations the extinction processes that can take place in
this system both in the well mixed case as well as on different types of
lattices. The different routes to extinction are revealed by the probability
distribution of the domination time, i.e. the time needed for one team to fully
occupy the system. If swapping is allowed between neutral partners, then the
probability distribution is dominated by very long-lived states where a few
very large domains persist, each domain being occupied by a mix of individuals
from species that form one of the teams. Many aspects of the possible
extinction scenarios are lost when only considering averaged quantities as for
example the mean domination time.
Journal of Statistical Mechanics Theory and Experiment 07/2013; 2013(08). DOI:10.1088/1742-5468/2013/08/P08011 · 2.40 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: In order to better understand the interplay of partnership and competition in population dynamics, we study a family of generalized May-Leonard models with N species. These models have a very rich structure, characterized by different types of space-time patterns. Interesting partnership formations emerge following the maxim that “the enemy of my enemy is my friend”. In specific cases cyclic dominance within coarsening clusters yields a peculiar coarsening behavior with intriguing pattern formation. We classify the different types of dynamics through the analysis of the square of the adjacency matrix. The dependence of the population densities on emerging pattern and propagating wave fronts is elucidated through a Fourier analysis. Finally, after having identified collaborating teams, we study interface fluctuations where we initially populate different parts of the system with different teams.
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics 03/2013; 87(3). DOI:10.1103/PhysRevE.87.032148 · 2.81 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Using numerical simulations we investigate the properties of the dynamic
phase transition that is encountered in the three-dimensional Ising model
subjected to a periodically oscillating magnetic field. The values of the
critical exponents are determined through finite-size scaling. Our results show
that the studied non-equilibrium phase transition belongs to the universality
class of the equilibrium three-dimensional Ising model.
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics 03/2013; 87(3). DOI:10.1103/PhysRevE.87.032145 · 2.81 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Using extensive Monte Carlo simulations we study the properties of the
non-equilibrium phase transition encountered in driven three-dimensional
Potts systems with magnetic friction. Our system consists of two
three-dimensional blocks, coupled through boundary spins, that move
along their boundaries with a constant relative velocity. Changing the
number of states in the system from two (Ising case) to nine states, we
find different scenarios for the surface behavior depending on whether
the bulk transition is continuous or discontinuous. In order to fully
assess the properties of this non-equilibrium phase transition, we vary
systematically the strength of the coupling between the two blocks as
well as the value of the relative velocity. For strong couplings between
the blocks the phase transition is found to be strongly anisotropic.
[Show abstract][Hide abstract] ABSTRACT: From complex biological systems to a simple simmering pot, thermodynamic
systems held out of equilibrium are exceedingly common in nature.
Despite this, a general theory to describe these types of phenomena
remains elusive. In this talk, we explore a simple modification of the
venerable Ising model in hopes of shedding some light on these issues.
In both one and two dimensions, systems attached to two distinct heat
reservoirs exhibit many of the hallmarks of phase transition. When such
systems settle into a non-equilibrium steady-state they exhibit numerous
interesting phenomena, including an unexpected ``freezing by heating.''
There are striking and surprising similarities between the behavior of
these systems in one and two dimensions, but also intriguing
differences. These phenomena will be explored and possible approaches to
understanding the behavior will be suggested.
[Show abstract][Hide abstract] ABSTRACT: Artificial antiferromagnets have attracted attention lately due to the
potential for technological applications. We model these systems as thin
Ising metamagnetic films and study their equilibrium properties using
Monte Carlo simulations. In variance with previous work but in agreement
with the experimental systems, we consider films comprised of ``sets''
of planes, with an antiferromagnetic coupling between sets and a
ferromagnetic coupling within sets. This allows us to consider different
situations by varying the number of planes in each set. Studying the
magnetization density and response functions as a function of
temperature and magnetic field, we determine the corresponding phase
diagrams. We discuss how a change of the number of planes in each set
changes the equilibrium phase diagram.